Picture Pie Fractions
In this lesson, children will identify parts of a whole and create pictures using a whole circle, a half circle, a quarter circle and an eighth of a circle.
(See Step 5: Adapt lesson for toddlers or preschoolers.)
Numbers and Operations
This lesson will help toddlers and preschoolers meet the following educational standards:
- Understand numbers, ways of representing numbers, relationships among numbers and number systems
- Represent and analyze mathematical situations and structures using algebraic symbols
- Understand meanings of operations and how they relate to one another
After this lesson, toddlers and preschoolers should be more proficient at:
- Connecting number words and numerals to the quantities that they represent, using various physical models and representations
- Understanding and representing commonly used fractions, such as 1/4, 1/3 and 1/2
- Using concrete, pictorial and verbal representations to develop an understanding of invented and conventional symbolic notations
- Counting with understanding and recognizing “how many” in sets of objects
- Understanding situations that entail multiplication and division, such as equal groupings of objects and sharing equally
Picture Pie Fractions
Lesson plan for toddlers/preschoolers
Step 1: Gather materials.
- The book: Picture Pie by Ed Emberley.
- Pre-cut, different-colored circles and parts of a circle (whole circles, half circles, fourths of a circle and eighths of a circle)
- Glue sticks, 12×18 pieces of construction paper and crayons or markers
- Chart paper for visuals during the lesson
Note: Small parts pose a choking hazard and are not appropriate for children age five or under. Be sure to choose lesson materials that meet safety requirements.
Step 2: Introduce activity.
- Explain to the children that today they are going to look at circles and parts that make up a circle. Explain that they will read a book called Picture Pie together and they will look at how a circle, divided like a pie, can be used to make pictures of all kinds.
- Ask the children about circles divided up like pies. Suggest: “Pizza pie”
Ask the following: “How many pieces do you usually divide a pizza pie into?” (8) “How many pieces make up a pizza pie?” (8) “How many pieces do you usually divide a round cake into?”
- Show the children a circle. Say: “This is a whole circle. Imagine that this is a pizza pie. All of the parts of the pie are still there. Nobody has taken a piece of pizza yet.”
- With the children watching, cut the circle in half. Say: “Now I am going to cut the circle in half. I am cutting the circle into two equal parts.” Place a whole circle up on the chart paper and then place the two halves next to or under the circle.
- You may want to use a visual for the children similar to the visual above. It is easier for the children to grasp the concept of parts of a whole if they can see all of the different ways that a circle can be divided and all of the parts of a circle that equal a whole.
Say: “If Billy and I were to share a pizza, we would divide it into two equal parts. We would divide the pizza pie in half so that we both had the same amount of pizza.”
- Show the children another circle. Ask: “How can we divide this circle into four equal parts?” Ask: “If this is a pizza pie and we have four people who want to share this pie, how can we divide this pie into four equal parts?”
- Show the children the process of first cutting the circle into half. Say: “I have two equal parts. I have cut the circle in half. Is this enough for four people?” (No) “What do I need to do to create two more pieces from these two halves?” (Cut those pieces in half)
- Show the process of cutting each half into fourths. Place the four fourths onto the chart paper next to the two halves. Say: “Now if Billy, Kim, Brian and I were to all share a pizza, we would need to cut it into four equal parts. We would cut the pizza into fourths.”
- Repeat steps 6-8 for eighths.
- With the chart paper containing the visual representations of a whole circle, two half circles, four fourths of a circle and eight eighths of a circle, start by explaining equal parts.
- Point to the halved circle, and say: “How many parts does this circle have?” (2) “Right, it has two parts. So we can say that two halves equal one circle. Is that right?”
- Say: “OK.” Ask: “But what about this circle?” Point to the circle divided into fourths. Say: “How many parts does this circle have?” (4) “Wow, you are right, it has four parts! So can we say that four fourths are equal to two halves and two halves are equal to one whole?”
- Ask: “Now what about the circle cut into eighths? Does this circle cut into eight equal parts equal the circle that is cut into four equal parts? Does it equal the circle that is cut into two equal parts? Does it equal a whole circle?” (Yes) “How can that be?” It is fun to act as if this discovery is something magical. Write down responses that the children might have on the chart paper.
- Read the book Picture Pie. There aren’t many words and the book reinforces the concept of halves, fourths and eighths of a whole circle. While looking at the book, have the children point out the parts of the circle. Say: “Look at this duck. It looks like it is made up of the various parts of a circle that we just discussed. Ask: “Can you point out the whole circle? Can you point out the half circle?” Do this for all of the parts of the circle.
Step 3: Engage children in lesson activities.
- Explain that now the children will make their own circle pictures or designs using various parts of a circle. Say: “I have cut up parts of a circle for you to use to create your own circle picture. You will be using whole circles, half circles, fourths of circles and eighths of circles. You can create anything that you would like and you can use crayons or markers as well. Glue the circles and circle parts onto your paper.”
- Encourage the children to use all of the parts of the circle in their collages. Say: “I see that you have used a half circle.” Ask: “Can you also use an eighth of a circle in your picture?”
- Display the children’s work.
- After using circles, you can use squares. Divide the square into halves, fourths and eighths. Compare the division of the square to that of the circle. The children can make collages using both the circles and the squares.
- Write the fraction equivalent onto each shape: 1 on the whole circle, 1/2 on the half circle, 1/4 on the fourth of the circle and 1/8 on the eighth of the circle. Explain that the bottom number (the denominator) tells you the number of parts the whole is divided into and the top number (the numerator) tells you the number of parts of the whole. So 1/8 is one part out of eight possible parts.
- By laying parts of the circle onto one another, you can discuss equivalent fractions. For example, two eights is equal to one quarter. Lay the two eighths on top of the fourth. Ask: “How many fourths do we need to make a half?” (2) Say: “So, we can say that two fourths are equal to one half.”
Step 4: Vocabulary.
- Divide: Group a number into equal parts
- Half: One of two equal parts of the shape
- Fourth: One of four equal parts of the shape
- Eighth: One of eight equal parts of the shape
- Equal: Exactly the same amount or value
- Whole: All of the parts or the total amount of something
Step 5: Adapt lesson for toddlers or preschoolers.
Adapt Lesson for Toddlers
- Not be able to conceptualize multiple fraction sizes in one lesson
- Not be able to manipulate the small circle pieces when creating their collages
Child care providers may:
- Just focus on halves of shapes to use for their collages (eliminate the fourths and the eighths from the discussion and from the options)
- Reinforce the concept of halving an object
Adapt Lesson for Preschoolers
- Be able to understand the concept of fraction equivalents
- Be able to understand the concept of equivalent fractions
Child care providers may:
- Write the fraction equivalent onto each shape: 1 on the whole circle, 1/2 on the half circle, 1/4 on the fourth of the circle and 1/8 on the eighth of the circle. Explain that the bottom number (the denominator) tells you the number of parts the whole is divided into and the top number (the numerator) tells you the number of parts of the whole. So 1/8 is one part out of 8 possible parts.
- By laying parts of the circle on top of one another, begin a discussion of equivalent fractions: two eighths is equal to one fourth. Lay the two eighths on top of the fourth. “How many fourths do we need to make a half?” (Two) “So, we can say that two fourths are equal to one half.”
- Picture Pie by Ed Emberley (New York: Little Brown Books for Young Readers)
- Picture Pie 2 by Ed Emberley (New york: Little Brown Books for Young Readers)
Music and Movement
- Any cooking activity helps to reinforce the concept of fractions. Bake cookies and use amounts such as half a cup of sugar, two cups of flour, etc. Allow the children to conceptualize the fraction and amounts and they can enjoy the final product as a yummy treat. If you are outside, you can pretend to cook by putting sand and water into the sensory tables. Add measuring cups and bowls with recipes designating how many cups (1, 1/2, 1/4, etc.) of water and sand to add to the bowl.
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